论文标题
拓扑矢量晶格中的无肢体概念
No-arbitrage concepts in topological vector lattices
论文作者
论文摘要
我们为拓扑矢量晶格中的无肢体概念提供了一个一般框架，该框架涵盖了许多众所周知的无容易概念概念。我们施加的主要结构条件是，具有初始财富的交易策略的结果和正面财富的人具有凸锥的结构。作为我们方法的结果，概念Nupbr，Naa $ _1 $和Na $ _1 $可能在我们的一般环境中可能不等于。此外，我们得出了资产定价基本定理（FTAP）的抽象版本，包括对Banach函数空间的抽象FTAP，并研究何时以分离度量以其经典形式保证FTAP。我们还考虑了一个具有半明星的金融市场，而该市场不需要具有数字，并得出结果，从而通过仅使用拓扑矢量晶格理论和随机分析的众所周知的结果，从而显示了无肢体概念之间的联系。
We provide a general framework for no-arbitrage concepts in topological vector lattices, which covers many of the well-known no-arbitrage concepts as particular cases. The main structural condition we impose is that the outcomes of trading strategies with initial wealth zero and those with positive initial wealth have the structure of a convex cone. As one consequence of our approach, the concepts NUPBR, NAA$_1$ and NA$_1$ may fail to be equivalent in our general setting. Furthermore, we derive abstract versions of the fundamental theorem of asset pricing (FTAP), including an abstract FTAP on Banach function spaces, and investigate when the FTAP is warranted in its classical form with a separating measure. We also consider a financial market with semimartingales which does not need to have a numéraire, and derive results which show the links between the no-arbitrage concepts by only using the theory of topological vector lattices and well-known results from stochastic analysis in a sequence of short proofs.
